State means at any particular time the values that an object hold. You can think it like an instance/object of a class holding some values at a particular time. So that is the state of that object. State transfer means transferring these values to a particular component.
REST is stateless because each request is self explanatory i.e. each request contains all the information that is needed by the requested resource and it does not depend on any previous state. Below link might help you on this...
https://looselyconnected.wordpress.com/2011/02/07/rest-what-is-state-anyway/